2D Can't possibly exist... we can't possibly exist

No, assuming that by thickness, he means me. :-(

 

So long as we're talking about a theoretical 2D in a vacuum fine but of course it doesn't exist. You can theoretically chase your tail as long as you like with increasing levels of precision.

What a real physicist would want to know what is/are the smallest complete 'thing/s' that could not be subdivided further.

When you try to think of that and then think, wait then, are those particles bound by a vacuum? Is so, why are there no new 'Big Bangs' happening along the edges of those particles? Maybe the universe is actually made of a 'infinitely fine and infinitely varied' 3D honeycomb / geodesic dome structure and it's density (energy/vibration frequencies) changes over time in different places in different ways. Maybe this unseen 3D honeycomb structure is the 'fabric of space' (as seen on Nova if you've seen those shows), the dark energy/dark matter, the gravity of the universe that we can't see. Rather than being a weak force, maybe gravity is a strong force. I'm no physicist though.

 

But measurements are just a way of describing thickness, like it doesn't matter how thick it is it, even if its too small for us to measure even if it is like a trillionth of a micron or whatever. Our units of measurements are just things we made up to make it easy to compare things.

 

Lets think about this like a coder. What is the z value of a Vector2? It is not 0, it is not even null. There is no value because nothing exists to have a value.

A very small number or even a 0 is not the same as the absence of a number.

 

But by this logic an atom (or smaller fundamental particle for sake of argument) is 0 dimensional because it can't have a smaller width, depth or height.

 

This is a fun thread. Here is my 2 cents to bring somethings to think about to the table. 1st, we most certainly do know that 2d stuff exists. Photons are an example. Energy, magnetic fields, etc are abstractions of "things" that we cannot see so we describe them as waves or similar.

The important thing to note here is that we cannot perceive them visually not because they aren't real but because we simply dont have the means. This is why we have multiple senses including hearing and touch. Our eyes cannot see everything.

Last, we basically know that 4th dimensions are plausible because the math works and not just that, we have done experiments that make no sense. For instance, quantum entanglement. We know it happens but the connection cannot exist in 3 dimensions nor 2 dimensions but that does not mean it is not real. We know its real.

The last piece of analogy I will give is this. Imagine a 2d character on a paper (lets just imagine for now). A 2d character on paper can look around the paper without any problems by turning. Now imagine that you, a 3d person, puts your finger directly in front of the 2d characters face. What does the 2d character perceive this as? From his perspective, all he sees is some black dot that appeared out of no where, He cannot possibly have any sort of explanation for such an event because he does not have any sort of way detecting anything in 3 space yet he knows that something outside the rules of his known universe happened. This is how I see quantum entanglement. Clearly, the evidence points to a very strong possibility of another dimension but due to our limitations (like the 2d character) we will never be able to perceive them or explain them.

 

I think we fail to separate our intuition of how things are measured from the reality of how things are when they are really small.

We super-impose the idea of measuring something onto our idea of that something. We can easily imagine a microscopic organism and drawing measurement lines with a pencil next to it, BUT, millions of those organisms could fit onto the tip of that pencil, so it couldn't possibly be drawing lines next to them, you would need a micro pencil to actually physically measure it.

Now consider something much smaller, like sub atomic particles or smaller. You need a very small pencil to physically measure them. If you don't physically hold something next to them to measure, you are just abstracting in your mind, like the pencil/micro-organism example. So maybe there is a smallest possible size of measurement that has nothing in existence that could measure it. You could not objectively measure it. Something with that thickness could be considered 2D, if such a thing could exist without the need for larger atoms or w/e to hold it together.

 

No it couldn't. Whether we have the tools required to measure it or not is completely beside the point. The scale of something doesn't change its dimensionality.

As I said before, the absence of a number is not the same as a very small number or a 0. Those are values, but we're talking about a lack of a value and, moreso, a lack of a property to assign a value to.

If I asked "What colour is the number 11?" is there any possible answer that could make sense? Numbers don't have a colour property. Similarly, a 2 dimensional shape doesn't have a size of its third dimension. If any shape has a size of a third dimension then it is necessarily 3D, by definition.

 

I think Khyrid explained it well with this already. We're getting towards the concept of infinity. The area under a curve is calculated using an integral, a theoretical dividing of the area into an infinite number of pieces. But can we really comprehend infinity. We can say that we do, but can we really grasp it? I would argue our finite selves cannot realistically comprehend infinity.

If we can't perceive, measure, or detect something, and there is no evidence of it, we can't prove that it exists. If the "dot" had not appeared on the 2d characters plane, that he can perceive or find evidence of, he would not have known it was there.

There is so much that we don't know, because we have no means by which to know it.

 

Couldn't we compare it to other things like, its 1/2 the size of an electron or something? I suppose what you say might be right but then we could never see or acknowledge its existence without being able to compare its size to something, even if its larger. And if that is the case then there is no way to know it exists?

 

But he didn't. He's picking an arbitrary number and saying "anything thinner than this is the same as having no thickness", which is incorrect. Just by having that property to be measured, regardless of its value, puts it in a completely different class of things than if the property weren't there to be measured.

 

That's exactly the point angrypenguin. It's a paradox. It's mind-boggling lol. "One unit of what?" is the right question to ask. The answer is, it's the unit of infintescimal smallness. Choose any unit. Now go smaller. Now take that unit and go smaller. Have we reached the smallest unit of measurement yet? Probably not, lets go smaller. Now divide it again. Now take that unit, and divide it again....................ad infinitum!

That's why it's a paradox. You might never reach the smallest unit one could possibly conceive.

That's why I go back to drinking my coke and watching some football lol

 

That's not what a paradox is.

Also, saying 'one unit of infinitesimal smallness' doesn't mean anything.

 

Hes crazy, but hes right.

 

I know what you're saying angrypenguin, that something in 2D has no thickness, and therefore cannot be measured. If it did, then it would cease to be in 2D and become 3D. I agree with you.

BUT, I thought we were talking about the fact that everything we call 2D, in reality, is displayed to us in 3D -- there is no true 2D in our 3D+ world. A 2D drawing on a piece of paper is still on a piece of paper that has thickness (however small). A 2D image on the computer screen is displayed from 3D material, and perceived by our 3D eyes. Atoms, no matter how small, have thickness. Whatever sub-atomic particle you can think of, probably has smaller sub-particles that we havn't grasped yet. That's what I was referring to pretty much. We may simply be arguing two different things.

Anyways, it's cool to think about, and if I'm wrong, I'm always up for learning .

 

How thick is a plane? The answer is 0. If you look at a 2D plane from any angle you would see nothing. If there were two 2D planes stacked on each other then you would surely see something? Yes? No? It depends on how thick the planes are, which still makes no sense.

Another things to throw into the mix is...

Ok so we have 5 senses... right? No not really, not technically at least. Sight, Hearing, Taste, Smell and Touch are the most well known senses. But the fact is that there is only one sense, Touch. Sight relies on light touching your eye. Hearing relies on waves of air (usually) or other things, such as water (when you are immersed in it). You get the idea.

But beyond that, we don't really even have the sense of touch. I was talking with a friend awhile back and he mentioned that atoms don't ever actually touch. Even the guy on VSauce mentions it. If you're sitting down on your chair, you (or your pants) never really touch the chair. You're not even touching yourself.

Now that the senses have been broken down, you can probably imagine that there are hundreds, possibly thousands, of possibilities for what other senses you can have. What else is there in the world to "sense"?

This may not seem like it relates to the topic, but in my mind it is all related. We all are a certain size and can detect/sense things at the specific size that they are. No more, no less. How much bigger/smaller can things possibly be?

 

If there are no people in a three-dimensional forest talking about dimensions and trying to prove whether two-dimensionality makes sense, does this thread even exist?

 

That's like asking, "If I have 3 dollars, can a chicken fly to the moon?"

 

If you're going to start going down the road of saying we only have one sense, then you need to define what touch is. And essentially, that would be receptors, which chemically change in response to light or electricity.

Since you're going down that route you might as well look at how electricity behaves, specifically electrons.

 

Haha, forgive me if I don't list out all the little details. I'm throwing my thoughts and ideas out so maybe others can build upon them or tear them apart. I'm a programmer that thinks way too much

 

2D exists, because your monitor displays completely flat data. It is not 3-dimensional, only the monitor is. The tiny pixels may be 3 dimensional, but they do not display a 3 dimensional image. They display a flat 2D image.

 

They don't display a 2D image. The pixels emit light, which is 3D. The data itself is also 3D because it exists on a 3D object which is then accessed by other 3D objects such as electricity, chips and whatnot. The idea of the data may seem 2D but in no way does it ever exist as 2D.

 

That's not correct.

While (for the most part) we describe geometry in three dimensions, the fourth dimension is relevant to us. Let me show you this with a simple example.

If we were to meet at some place, giving you the coordinates (first three dimensions) wouldn't be enough. You'd be asking me when to meet. So you'd be asking me about the fourth dimension - time. And there goes your "[...]These multi-dimensions past 3 are fictions[...] theory.

Your argumentation boils down to "I don't need it IRL, so it's not relevant.", which is nonsense. When arguing like this we could dismiss the complex numbers because they make no sense in everyday life. "Why the hell is the square-root of -1 i?". The complex numbers, however, have relevance in technology so dismissing them would be a huge step backwards.



To get back on topic:
Nice theory, but it's wrong.
superpig has already said it before, but since this thread seems to go on, I'll repeat it.
Your entire argumentation is based on the fact there is a paradoxon concerning the height. However, we're talking about a two dimensional plane here. There is no such thing as "height" in a two dimensional world, because the height is the third dimension.

You're trying to apply a three dimensional concept on a two dimensional world, of course it doesn't work.

 

2D is nothing but a mathematical simplification of space, so is 3D. X, Y and Z is only something that we puny humans use to describe it with. If you think there cant be a 4th or nth dimension you are dead wrong. In fact every time you are rotating an object in Unity you are using the 4th dimension in the form of Quaternions . According to the Theory of Relativity, measurements of various quantities are relative to velocities of observers. In particular, space and time can dilate. Therefore using simply Vector3.Distance to measure distances in astronomical scale would be insufficient as there are dimensions it does not account for.

 

Nope.

The dimensionality of a transmission medium is not the same as the dimensionality of the transmitted data.

 

The correct reply to this thread would have been: 2D can't possibly exist until Unity 4.3!

 

Of course you can apply transforms to a 2D plan to create an object in a 3D world and then transforms on that 3D object in a 3D world don't change that it's a 3D world. A 3D transform at point t is a 3D world. Time is a measure; not a dimension you can travel backwards through. You go forward and always at the same rate so it's rather similar to the theoretically perfect 2D world that you can demand as much or little precision as you like but time is still advancing forward at the same rate. Driving faster to get to work isn't speeding up time. It's driving faster. That is the mistake being made here.

Time is a measure indicative of life. It's not a dimension that can be changed as a 3D world can be changed.

Queue up the Sprockets videos.

 

Our inability to change it doesn't make it any less relevant. Time isn't a spatial dimension, but it's widely considered and/or treated as a 4th dimension for plenty of practical purposes. And we are travelling through time (or, equivalently, it is travelling around us), we just can't control it.

 

http://en.wikipedia.org/wiki/Time_dilation

 

Aww man I was trying to forget about that.

 

It is a paradox.

http://plato.stanford.edu/entries/paradox-zeno/#ArgComDiv

2.3 The Argument from Complete Divisibility

 

The relevance of using time to measure deltas in a 3D world doers not make time a dimension itself. Time is not a dimension, it's indicative of intelligence measuring deltas in a 3D world.

 

As I stated, the progress of time does not change but the means by which we attempt to measure time can and do change. Time hasn't dilated: the 3D natural effects we use to measure time have changed thus invalidating our measure of time. Our 3D mechanical equipment is simply incapable of measure some types of forces acting to create these time dilation effect. That's not to say theoretically they can't attribute those effects to some unseen force but they can't attribute it to time slowing down or speeding up just like I can't claim I turned back time by flipping on a light switch at night.

 

Theoretically such a unit would be infinitely dense were it not a vacuum and so that unit and the surrounding vacuum would constitute the initial conditions proposed in the Big Bang theory and to avoid an infinite number of subsequent Big Bangs the universe would need to be a mesh of varyingly dense interconnected geodesic / web type filaments vibrating at different energy levels.

 

Well, there's no way to disprove what you proposed. But how do you know that it is, in fact some invisible force and not time dilating?

 

If you use a quartz crystal to measure time and that crystal's vibration rate changes due to heat and thus time slows down or speeds up is the type of known effect what the time dilation theory ignores. Measures are as good as the impunity to outside forces of the measure. If impunity is violated the measure is invalidated.

I trust a ruler before I trust my feet to measure a foot and likewise in the last century time keeping has reached a whole new level of sophistication because it is inherently an artificial measurement and hence an indication of intelligence and not a dimension.

I'm no physicist and so trust me when I say I'm not calling anybody dumb when I disagree with some famous theory. I'm suggesting they are wrong in using a clearly man-made measure's unexpected variance as being the culprit when then should use it indicate an unknown force acting on another force that we can measure. They can use the unexpected variance of the man-made measure to indicate the presence of the unknown force. I believe they are doing similar to measure gravity and they indeed are using time's variance as an indication of this unknown force. They are being misleading if they say a unit of time is varying. It is not. The instruments used to attempt to measure time are varying. Huge difference. Since they using deltas in 3D systems to measure time it's always going to appears as if time can speed up or slow down. It cannot. The 3D systems used to estimate time can speed up or slow down. Most of us probably know the rotation of the earth is slowing down and it is revolution around the sun is speeding up and those are the 2 long standing tradition measures of time but it's the mechanical system that's changed. A unit of time should be constant to avoid ignoring unknown forces in physicists equations.

So in my mind, if they were to replace time or rather keep it constant in all those equations with an unknown force then they'd get more accurate model of the universe. To do this they need to make that famous 'cosmological constant' variable and have time serve as the new 'cosmological constant'.

So Star Trek, Star Wars, and Dr No are entertaining at times but time travel is only possible in a forward direction.

 

Heisenberg would be saddened at the non-believers of a quantum world.

 

I love the way people are so sure of there ideas, everyone is so into thinking there idea is right that they lose any possibility of something else being true. Lots of people do this, including most of the scientific world and nearly every teacher I've ever seen, In the end this will ultimately hold us back as a species (Well, it already has).

 

I'm about as sure that my ideas are correct as I'm sure that my code will work the first time after coding it for an hour without testing

 

So, pretty sure ?

 

I'm 100% sure until I test and get lots of errors

 

IMO, 2D is just a point of view, it's not what you are but what you see

The world, the life are not in 3D but in xD , there is multiple definition of what you see, what you represent and how you are represented

Just like the infinite small and infinite large, as for infinite numbers, they are not defined, as dimention they are not defined too

The world is just about perception, from each part of each PoV because the world is just a imagination of something, wich result of infinite "things"

Yeah i know i'm crazy


Edit :

A day i asked my teacher :

Me: Infinite exist ?
Teacher : Yes!
Me: but, for example, from A to B there is a distance, i need to travel half of the distance to get to B
so it's like : A >a'>B
but to get to a' i need to travel half of the distance
so it's like A>a''>a'>B
but to get to a'' i need to travel half of the distance
so it's like A>a'''>a''>a'>B
etc..

So how can i go to B if i always need to travel half of all half of distance ?
You are right then, infinite exist
BUT how can i manage to come back from School to Home it's like on the example but how this 2 similar example have different result ?



It's all about perception of scale, time and point of view